Publikationen
2023
Gennadiy Averkov, Matthias Schymura
On the Maximal Number of Columns of a Δ-modular Integer Matrix: Bounds and Computations
to appear in Math. Programming, 2023
Gennadiy Averkov, Christopher Hojny, Matthias Schymura
Efficient MIP techniques for computing the relaxation complexity
Math. Programming Computation, online first, 2023
Code on github for computing the relaxation complexity
Gennadiy Averkov, Ivan Soprunov
Plücker-type inequalities for mixed areas and intersection numbers of curve arrangements
International Mathematics Research Notices, online first, 2023
2021
Gennadiy Averkov, Matthias Schymura
Complexity of linear relaxations in integer programming
publizierte Version: https://www.math.b-tu.de/INSTITUT/algmath/documents/averkov/Averkov-Schymura2021_Article_ComplexityOfLinearRelaxationsI-2.pdf
Archiv_Preprint: https://arxiv.org/abs/2003.07817
Gennadiy Averkov
Equality Case in van der Corput's Inequality and Collisions in Multiple Lattice Tilings
http://link.springer.com/article/10.1007/s00454-019-00089-8
Gennadiy Averkov, A. Chavez, J.A. De Loera, B. Gillespie
The lattice of cycles of an undirected graph
https://www.sciencedirect.com/science/article/abs/pii/S0024379520305103
2020
Gennadiy Averkov, Christopher Borger, Ivan Soprunov
Inequalities between mixed volumes of convex bodies: volume bounds for the Minkowski sum
https://arxiv.org/abs/2002.03065
Gennadiy Averkov, Anastasia Chavez, Jesus A. De Loera, Bryan R. Gillespie
The lattice of cycles of an undirected graph
https://arxiv.org/abs/2002.01001
2019
Iskander Aliev; Gennadiy Averkov; Jesús A. De Loera; Timm Oertel
Optimizing Sparsity over Lattices and Semigroups
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 11 S., 2019
https://arxiv.org/abs/1912.09763
Gennadiy Averkov; Johannes Hofscheier; Benjamin Nill
Generalized flatness constants, spanning lattice polytopes, and the Gromov width
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 11 S., 2019
https://arxiv.org/abs/1911.03511
Gennadiy Averkov
Second-order cone representable slices of the positive semidefinite cone of size three
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 7 S., 2019
https://arxiv.org/abs/1909.08937
Gennadiy Averkov; Giulia Codenotti; Antonio Macchia; Francisco Santos
A local maximizer for lattice width of 3-dimensional hollow bodies
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 8 S., 2019
https://arxiv.org/abs/1907.06199
Gennadiy Averkov; Christopher Borger; Ivan Soprunov
Classification of triples of lattice polytopes with a given mixed volume
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 61 S., 2019
https://arxiv.org/abs/1902.00891
Gennadiy Averkov; Benjamin Peters; Sebastian Sager
Convexification of polynomial optimization problems by means of monomial patterns
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 36 S., 2019
https://arxiv.org/abs/1901.05675
Emily Speakman; Gennadiy Averkov
Computing the volume of the convex hull of the graph of a trilinear monomial using mixed volumes
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 18 S., 2019
https://arxiv.org/abs/1810.12625
2018
Averkov, Gennadiy; Basu, Amitabh; Paat, Joseph
Approximation of corner polyhedra with families of intersection cuts
In: SIAM journal on optimization/ Society for Industrial and Applied Mathematics - Philadelphia, Pa.: SIAM, Bd. 28.2018, 1, S. 904-929
https://doi.org/10.1137/17M1128939
Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin
Lattice simplices with a fixed positive number of interior lattice points - a nearly optimal volume bound
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 2018
https://arxiv.org/abs/1710.08646
Averkov, Gennadiy; Kaibel, Volker; Weltge, Stefan
Maximum semidefinite and linear extension complexity of families of polytopes
In: Mathematical programming: Series A, Series B ; a publication of the Mathematical Programming Society - Berlin: Springer, Bd. 167.2018, 2, S. 381-394
https://doi.org/10.1007/s10107-017-1134-7
2017
Averkov, Gennadiy; González Merino, Bernardo; Paschke, Ingo; Schymura, Matthias; Weltge, Stefan
Tight bounds on discrete quantitative Helly numbers
In: Advances in applied mathematics - Amsterdam [u.a.]: Elsevier, Bd. 89.2017, S. 76-101
https://doi.org/10.1016/j.aam.2017.04.003
Averkov, Gennadiy; Amitabh, Basu; Paat, Joseph
Approximation of corner polyhedra with families of intersection cuts
In: Integer Programming and Combinatorial Optimization - Cham: Springer, S. 51-62, 2017 - (Lecture Notes in Computer Science; 10328)
https://doi.org/10.1007/978-3-319-59250-3_5
2016
Averkov, Gennadiy; Langfeld, Barbara
Homometry and direct-sum decompositions of lattice-convex sets
In: Discrete & computational geometry: an international journal of mathematics and computer science - New York, NY: Springer, Bd. 56.2016, 1, S. 216-249
https://doi.org/10.1007/s00454-016-9786-2
Averkov, Gennadiy; Kaibel, Volker; Weltge, Stefan
Maximum semidefinite and linear extension complexity of families of polytopes
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 11 S., 2016
https://doi.org/10.1007/s10107-017-1134-7
Averkov, Gennadiy; Krümpelmann, Jan; Weltge, Stefan
Notions of maximality for integral lattice-free polyhedra - the case of dimension three
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 45 S., 2016
https://arxiv.org/abs/1509.05200
Averkov, Gennadiy; Merino, Bernardo González; Henze, Matthias; Paschke, Ingo; Weltge, Stefan
Tight bounds on discrete quantitative Helly numbers
In: De.arxiv.org - [S.l.]: Arxiv.org, insges. 19 S., 2016
https://arxiv.org/abs/1602.07839
2015
Averkov, Gennadiy; Bianchi, Gabriele
Covariograms generated by valuations
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 19, S. 9277-9329, 2015
https://doi.org/10.1093/imrn/rnu219
Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin
Largest integral simplices with one interior integral point - solution of Hensley's conjecture and related results
In: Advances in mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 274.2015, S. 118-166, 2014
https://doi.org/10.1016/j.aim.2014.12.035
Averkov, Gennadiy; Basu, Amitabh
Lifting properties of maximal lattice-free polyhedra
In: Math. Program., Vol. 154, 2015, Issue 1-2, Ser. B, S. 81--111, ISSN 0025-5610, 10.1007/s10107-015-0865-6
https://doi.org/10.1007/s10107-015-0865-6
2014
Averkov, Gennadiy; Basu, Amitabh
On the unique-lifting property
In: Integer programming and combinatorial optimization. - Cham [u.a.] : Springer, S. 76-87, 2014 - (Lecture notes in computer science; 8494)
https://doi.org/10.1007/978-3-319-07557-0_7
2013
Averkov, Gennadiy
Constructive Proofs of some Positivstellensätze for Compact Semialgebraic Subsets of R d
In: Journal of optimization theory and applications. - Dordrecht [u.a.] : Springer Science + Business Media, Bd. 158.2013, 2, S. 410-418
https://doi.org/10.1007/s10957-012-0261-9
Averkov, Gennadiy
On maximal S-free sets and the helly number for the family of S-convex sets
In: SIAM journal on discrete mathematics. - Philadelphia, Pa : Soc, Bd. 27.2013, 3, S. 1610-1624
https://doi.org/10.1137/110850463
Averkov, Gennadiy; Conforti, Michelle; Del Pia, Alberto; Di Summa, Marco; Faenza, Yuri
On the convergence of the affine hull of the Chvátal-Gomory closures
In: SIAM journal on discrete mathematics. - Philadelphia, Pa : Soc, Bd. 27.2013, 3, S. 1492-1502
https://doi.org/10.1137/120898371
Averkov, Grennadiy
A proof of Lovászs theorem on maximal lattice-free sets
In: Beiträge zur Algebra und Geometrie. - Berlin : Springer, Bd. 54.2013, 1, S. 105-109
https://doi.org/10.1007/s13366-012-0092-8
2012
Averkov, Gennadiy; Wagner, Christian
Inequalities for the lattice width of lattice-free convex sets in the plane
In: Beiträge zur Algebra und Geometrie. - Berlin : Springer, Bd. 53.2012, 1, S. 1-23
https://doi.org/10.1007/s13366-011-0028-8
Averkov, Gennadiy; Bröckner, Ludwig
Minimal polynomial descriptions of polyhedra and special semialgebraic sets
In: Advances in geometry. - Berlin [u.a.] : de Gruyter, Bd. 12.2012, 3, S. 447-459
https://doi.org/10.1515/advgeom-2011-059
Averkov, Gennadiy
On finitely generated closures in the theory of cutting planes
In: Discrete optimization. - New York, NY [u.a.] : Elsevier, Bd. 9.2012, 4, S. 209-215
https://doi.org/10.1016/j.disopt.2012.06.003
Averkov, Gennadiy; Langfeld, Barbara
On the Reconstruction of Planar Lattice-Convex Sets from the Covariogram
In: Discrete & computational geometry. - New York, NY : Springer, Bd. 48.2012, 1, S. 216-238
https://doi.org/10.1007/s00454-012-9416-6
Averkov, Gennadiy
On the size of lattice simplices with a single interior lattice point
In: SIAM journal on discrete mathematics. - Philadelphia, Pa : Soc, Bd. 26.2012, 2, S. 515-526
https://doi.org/10.1137/110829052
Averkov, Gennadiy; Weismantel, R.
Transversal numbers over subsets of linear spaces
In: Advances in geometry. - Berlin [u.a.] : de Gruyter, Bd. 12.2012, 1, S. 19-28
https://doi.org/10.1515/advgeom.2011.028
2011
Averkov, Gennadiy; Bey, Christian
Description of polygonal regions by polynomials of bounded degree
In: Monatshefte für Mathematik. - Wien [u.a.] : Springer, Bd. 162.2011, 1, S. 19-27
https://doi.org/10.1007/s00605-010-0224-x
Averkov, Gennadiy; Henk, Martin
Representing simple d-dimensional polytopes by d polynomials
In: Mathematical programming / A - Berlin: Springer, Bd. 126.2011, 2, S. 203-230
https://doi.org/10.1007/s10107-009-0280-y
2010
Averkov, Gennadiy
On nearly equilateral simplices and nearly l 8 spaces
In: Canadian mathematical bulletin . - Toronto : Univ. of Toronto Press, Bd. 53.2010, 3, S. 394-397
https://doi.org/10.4153/CMB-2010-055-1
2009
Henk, Martin; Averkov, Gennadiy
Three-dimensional polyhedra can be described by three polynomial inequalities
In: Discrete & computational geometry. - New York, NY : Springer, Bd. 42.2009, 2, S. 166-186
https://doi.org/10.1007/s00454-009-9183-1